Mg(OH)2 ⇆ Mg²⁺ + 2 OH⁻

The exothermic dissolution of Mg(OH)2(s) in water is represented by the equation above. The Kₛₚ of Mg(OH)2 is 1.8 x 10⁻¹¹.
Which of the following changes will increase the solubility of Mg(OH)2 in an aqueous solution?

a) Decreasing the pH
b) Increasing the pH
c) Adding NH3 to the solution
d) Adding Mg(NO3)2 to the solution

a) Decreasing the pH

Explanation:

What we need to know to solve this problem is that we have an equilibrium for the dissolution of Mg(OH)₂ and we are bringing changes and need to know which one will increase the solubility of this hydroxide.

From LeChateliers principle we know that after any change brought to the equilibrium, the system will react in such a way as to restore the equilibrium by minimizing the disturbance.

Lets see now how our equilibrium will react for the given changes:

a) Decreasing pH

Decreasing pH effectively means we are adding acid to the equilibrium. This acid will consume part of the hydroxide ion, and the system will then shift to to the production of some hydroxide to restore equilibrium.

Therefore Mg(OH)₂ will become more soluble.

b) Increasing the pH

Increasing the pH will have the opposite effect as in part A, and will shift the equilibrium to the reactant side  precipitating some Mg(OH)₂

c) Adding NH₃

NH₃ is a weak base therefore it  will produce some hydroxide ion governed  by the equilibrium

NH₃ + H₂O ⇆ NH₄⁺ + OH⁻

Therefore the equilibrium will shift in the same manner as in part b), that is precipitating some Mg(OH)₂.

d) Addig Mg(NO₃)₂

Here we will be adding Mg²⁺ to the equilibrium, and the system will react to remove some of the added Mg²⁺ making the Mg(OH)₂ less soluble.

the answer is true.